1D random walks based on the digits of in various bases. If is even, a step to the right is taken, if is odd, a step to the left is taken.

1D random walks based on the digits of in various bases. If is even, a step to the right is taken, if is odd, a step to the left is taken. The left graphic shows the average distance of the walker from the origin, averaged over the first 100 even bases . The right graphic shows the binned scaled deviation of the individual walks (for a fixed basis ) from the average.